Depends on the individual circumstances really but the basics would be (assuming the title to the lease is already registered at the Land Registry which it should be if dated 2009) the ID the Land Registry need, original signed transfer deed (keep a copy, preferably certified by a solicitor!). I'd also send a copy and ask for the original back), SDLT certificate (even if none payable) and the relevant Land Registry fee.
If there was a charge on the property (eg mortgage, charging order) then you would need to send the relevant discharge documentation from the chargeholder for each charge to be removed.
Did you do any checks before buying as to any charges (or other restrictions) on the property and have they definitely been discharged and do you have the discharge/removal documentation? Did you do any of the usual pre-completion searches to ensure that your registration is protected and the seller isn't bankrupt or about to be (unless sold by receiver/lender who has repossesed or similar)?
There may also be obligations in the lease that need to be complied with before any change of ownership at the LR can take place eg consent from a superior Landlord (Landlord's Landlord) or management company. Did you look into any of this?
I would assume you have not got a "usual" mortgage on it as it doesn't sound like you used a legal advisor as most lenders would demand but, if there is any charge to be secured over the property (eg private loan) then the relevant original signed charged documentation would also need to be sent.
Sorry for raising a load more questions but there are all sorts of potential issues which are unknown without seeing all the title and docs.
Do you have access to a legal advisor who could look over things for you and make sure it's done right and advise of any potential issues which could try to be resolved sooner rather than later? Make sure you're properly protected.